Exploring Albert Rijksbaron's book, The Syntax and Semantics of the Verb in Classical Greek: An Introduction, to see how it would need to be adapted for Koine Greek. Much of the focus will be on finding Koine examples to illustrate the same points Rijksbaron illustrates with Classical examples, and places where Koine Greek diverges from Classical Greek.

On questions of tense and aspect generally, Rijksbaron plays up tense and plays down aspect to a greater extent than most others would nowadays (p. 2, n. 1). On the one hand, it's convenient to speak in tense-based terms of anteriority and simultaneity when discussing the relationship between a participle and the main verb (p. 117); on the other hand, this causes problems for Rijksbaron when he looks at the gnomic aorist (p. 32). Such aorists are much easier to explain if the aorist indicative fundamentally marks perfective aspect rather than past tense. (The anteriority and simultaneity expressed by aorist and present participles respectively can still be easily explained in aspect-based accounts as epiphenomenal.) Significantly, the gnomic aorist which causes him such difficulty comes from Homer, whereas the vast majority of his examples come from Herodotus and Classical Attic (the index locorum contains only two citations from Homer). Based on the late development of the historical present (which, quite the opposite of the gnomic aorist, is easier to explain in a tense-based model like Rijksbaron's than in an aspect-based one), it seems likely, as I argued in a talk at the 2008 APA, that tense gradually became more important relative to aspect over the years between Homer and the classical period. Rijksbaron's focus on the fifth and fourth centuries would then explain his bias in favor of tense.

It is curious that he feels that the historical present is less of a problem than the gnomic aorist with a tense based model, for that is the camel's nose under the tent for the tenseless approach. George has a recent essay about it, which I haven't seen, that may explain his thinking: "The temporal characteristics of the historical present in Thucydides," in The Historical Present in Thucydides: Semantics and Narrative Function, ed. J. Lallot, A. Rijksbaron, B. Jacquinod, and M. Buijs (Brill, 2011)